SOLUTION: y=x^(7/2) - 7x^2, x>0 Find critical points

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Question 1181030: y=x^(7/2) - 7x^2, x>0
Find critical points
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

Critical points are points where the function is defined and its derivative is zero or undefined.
y=x%5E%287%2F2%29+-+7x%5E2, x%3E0
derivate:
y'%28x%29+=+%287%2F2%29x%2A+%28x%5E%283%2F2%29+-+4%29
%287%2F2%29x%2A+%28x%5E%283%2F2%29+-+4%29=0
=>%287%2F2%29x=0=>x=0=> exclude because given x%3E0
=>x%5E%283%2F2%29+-+4=0=>x%5E%283%2F2%29+=+4=>sqrt%28x%5E3%29+=+4
=>x%5E3+=+16=>x+=+2%2A+2%5E%281%2F3%29

Critical point is at x+=+2%2A+2%5E%281%2F3%29.